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Abstract Entangled matter provides intriguing perspectives in terms of deformation mechanisms, mechanical properties, assembly and disassembly. However, collective entanglement mechanisms are complex, occur over multiple length scales, and they are not fully understood to this day. In this report, we propose a simple pick-up test to measure entanglement in staple-like particles with various leg lengths, crown-leg angles, and backbone thickness. We also present a new “throw-bounce-tangle” model based on a 3D geometrical entanglement criterion between two staples, and a Monte Carlo approach to predict the probabilities of entanglement in a bundle of staples. This relatively simple model is computationally efficient, and it predicts an average density of entanglement which is consistent with the entanglement strength measured experimentally. Entanglement is very sensitive to the thickness of the backbone of the staples, even in regimes where that thickness is a small fraction (< 0.04) of the other dimensions. We finally demonstrate an interesting use for this model to optimize staple-like particles for maximum entanglement. New designs of tunable “entangled granular metamaterials” can produce attractive combinations of strength, extensibility, and toughness that may soon outperform lightweight engineering materials such as solid foams and lattices. 

Randomly distributed granular materials offer a rich landscape of mechanisms but their tunability is limited. Taking inspiration from crystallography and granular mechanics, we fabricated and tested fully dense cohesive FCC and HCP granular crystals, and developed granular crystal plasticity models to investigate their relative strength and deformation mechanisms. Geometrically, switching from FCC to HCP is remarkably simple and only involves a 60° rotation about the midplane of individual dodecahedral grains. However, the effect of this transformation on crystallography, properties and mechanics are profound. This rotation breaks several symmetries, and while additional slip systems are made available (prismatic, pyramidal.) compared to the {111} family in FCC, each of the families in HCP contain a smaller number of total slip planes. As a result, slip in HCP is in general more difficult to activate resulting in an average strength 50% greater than in FCC. We also observed mechanisms that are unique to granular crystals: micro-buckling in FCC and HCP, and splaying in HCP crystals loaded along the c-axis. These granular crystals offer powerful and versatile platforms for new generation mechanical metamaterials with tunable inelastic deformation, energy absorption and strength. For example, the granular architecture amplifies the properties of the adhesive by about one order of magnitude, so that attractive rheologies maybe be translated into useful responses in compression. 

Entangled matter displays unusual and attractive properties and mechanisms: tensile strength, capabilities for assembly and disassembly, damage tolerance. While some of the attributes and mechanisms share some traits with traditional granular materials, fewer studies have focused on entanglement and strength and there are large gaps in our understanding of the mechanics of these materials. In this report we focus on the tensile properties and mechanics of bundles made of staple-like particles, and particularly on the effect of adjusting the angle between the legs and the crown in individual staples. Our experiments, combined with discrete element models, show competing mechanisms between entanglement strength and geometric engagement between particles, giving rise to an optimum crown-leg angle that maximizes strength. We also show that tensile forces are transmitted by a small fraction of the staples, which is organized in only 1-3 force chains. The formation and breakage of these chains is highly dynamic: as force chains break, they are replaced by fresh ones which were previously mechanically invisible. Entangled matter offers interesting perspectives in terms of materials design which can lead to unusual combination of properties: simultaneous strength and toughness, controlled assembly and disassembly, re-conformability, recyclability. 

Typical granular materials are far from optimal in terms of mechanical performance: Random packing leads to poor load transfer in the form of thin and dispersed force lines within the material, to inhomogeneous jamming, and to strain localization. In addition, localized contacts between individual grains result in low stiffness, strength and brittleness. Here we propose a granular material that simultaneously embodies three approaches to increase strength: geometrical design of individual grains, crystallization, and infiltration by an adhesive. Using mechanical vibrations, we assembled millimeter-scale 3D printed grains with rhombic dodecahedral shapes into fully dense FCC granular crystals. We then infiltrated the granular structure with a tacky, polyacrylic adhesive that is orders of magnitude weaker than the grains, but which provides sustained adhesion over large interfacial displacements. The resulting material is a fully dense, free-standing space filling granular crystal. Compressive tests show that these granular crystals are up to 60 times stronger than randomly packed cohesive spheres and they display a rich set of mechanisms: Nonlinear deformations, crystal plasticity reminiscent of atomistic mechanisms, cross-slip, shear-induced dilatancy, micro-buckling, and tensile strength. To capture some of these mechanisms we developed a multiscale model that incorporates local cohesion between grains, resolved shear and normal stresses on available slip planes, and prediction of compressive strength as function of loading orientation. The predicted strength is highly anisotropic and agrees well with the compression experiments. Once fully understood and harnessed, we envision that these mechanisms will lead to granular engineering materials with unusual combinations of mechanical performances attractive for many applications.